I was asked by Roger why a saxophone goes flat when it is cold. I speculated about changing bore size, but could not immediately come up with a plausible explanation. Trip contacted some boffins at Clair Brothers ( they supply the tour sound system ) who put me straight. A simplified explanation is as follows :

The velocity of sound through air is proportional to the temperature of the air the sound is travelling through.

The resonant frequency ( tuning ) of a fixed tube is proportional to the velocity of sound.

Therefore the resonant frequency (tuning ) of the saxophone on any given note is proportional to the air temperature passing through it.